Solvus lines

Identification of unknown crystal structures and determination of phase fields by X-rays can be problematical if the characteristic patterns of the various phases are quite similar, for example in some b.c.c. A2-based ordered phases in noble-metal-based alloys. However, in many cases the characteristic patterns of the phases can be quite different and, even if the exact structure is not known, phase fields can still be well established. Exact determination of phase boundaries is possible using lattice-parameter determination and this is a well-established method for identifying solvus lines for terminal solid solutions. The technique simply requires that the lattice parameter of the phase is measured as a function of composition across the phase boimdary. The lattice parameter varies across the single-phase field but in the two-phase field becomes constant. Figure 4.12 shows such a phase-boundary determination for the HfC(i i) phase where results at various temperatures were used to define the phase boundary as a fimction of temperature (Rudy 1969). As can be seen, the position of is defined exactly and the method can be used to identify phase fields across the whole composition range. 

Again, providing the various H and S terms are temperature-independent, the solution remains exact and provides a rapid method of calculating the liquidus temperature. Equation (9.10) is generally applicable to any phase boundary between a solution phase and stoichiometric compound, so could equally well be used for solid-state solvus lines. 

The Cu-Zn system (see Figure 2.7) displays a number of intermediate solid solutions that arise due to limited solubility between the two elements. For example, at low wt% Zn, which incidently is the composition of alloys known as brass, the relatively pure copper a phase is able to accommodate small amounts of Zn as an impurity in the crystal structure. This is known as a terminal solid phase, and the solubility limit where intermediate solid solutions (such as a + /S) begin to occur is called the solvus line. Some of the three-phase transformations that are found in this diagram include a peritectic (5 - - L -> e) and a eutectoid (5 -> y - - e). Remember that these three-phase transformations are defined for equilibrium coohng processes, not heating or nonequihbrium conditions. 

In many cases, there is partial solid solubility between the pure components of a binary system, as in the Pb-Sn phase diagram of Figure 11.5, for example. The solubility limits of one component in the other are given by solvus lines. Note that the solid solubility limits are not reciprocal. Lead will dissolve up to 18.3 percent Sn, but Sn will dissolve only up to 2.2 percent Pb. In Figure 11.5, there are two two-phase fields. Each is bounded by a distinct solvus and liquidus line, and the common sofidus line. One two-phase field consists of a mixmre of eutectic crystals and crystals containing Sn solute dissolved in Pb solvent. The other two-phase field consists of a mixture of eutectic crystals and crystals containing Pb solute dissolved in Sn solvent. 

By employing the lever mie, a tie line may be used to determine the fractional amounts of the phases present. For example, a tie line can be drawn in Figure 11.6 below the solidus and between the a and /3 solvus lines to determine the fractions of those two components in the (a, /3) solid solution /" and/. Since/" -F/ = 1, the percentages of the two phases present at any point, x, on the tie line is calculated as follows ... 

When the stable boundaries of an equilibrium phase diagram are extended as, for example, in Figure 11.14, regions of metastability are shown. In eutectic systems (Fig. 11.14fl), metastable equilibria of the solvus lines usually form a liquid miscibility dome. On the other hand, as illustrated in Figure 11.14/7, metastable extensions of... 

Figure 11.14. Metastable extensions of equilibrium-phase boundaries. Solvus line extensions usually form a liquid miscibility dome. Extensions of incongruently melting compounds form a congruent melting point and extensions of congruently melting compounds often form eutectics with non-neighboring phases.

Recalling the earlier discussion of the disappearing-phase x-ray method of locating a solvus line (Sec. 12-4), we note from Eq. (14-12) that the intensity ratio /y// is not a linear function of the volume fraction Cy, or, for that matter, of the weight fraction h. ... 

Fig. 10 Thermodynamic and kinetic basis for solute depletion in the case of a binary alloy consisting of solvent A and solute B. (a) Binary equilibrium phase diagram with complete miscibility in the liquid state, partial miscibility in the solid state given by existence of a terminal solid solution. Cs is the composition along the solvus line. is the overall composition of the alloy, (b) Time-temperature-transformation diagram for precipitation of in an a matrix for the alloy shown in (a) with overall composition,...

FIGURE 8.2 Patametric method for detetmination of the solvus lines in a binary phase diagram. 

The phase boundaries of the Pd-X (X = H,D,T) system were determined from pressure concentration temperature data because of the high risk of handling PdT samples outside our tritium loading equipment. Pd forms no stable oxide layers as is the case for or Nb that prevent the tritium to leave the sample. The boundaries between the miscibility gap and the 3-phase were obtained from the shape of the desorption isotherms. The values of concentration and temperature of the solvus line between the a- and the two phase regions a+3 were obtained by quasi isochoric measurements. A PdX sample with the concentration x slightly in the miscibility gap was heated in small temperature steps so that the concentration of the sample decreased and finally belonged to the pure a-phase. The change of slope in the equilibrium pressure as a function of the inverse temperature is interpreted as the intersection with the solvus line. 

They found that both the transition and melting point variations with alloying exhibited a minimum, but no separation of the liquidus-solidus and the two solvus lines were observed. 

The phase diagram for the Gd-Dy system as presented by Markova et al. showed six data points that formed a smooth curve defining the solidus of the system. This solidus has a slight downward curvature and the liquidus was drawn as a dashed straight line that connected the melting points of the end-members. Dashed solvus lines having a small gap between them indicated the probable temperature-composition relationship for the hep bcc transformation but no data were presented in support of these lines. 

Shiflet et al. (1979) calculated the phase diagram for this system using the Kaufman method. The calculated Uquidus and solidus lines and the solvus lines that define the two-phase field at the bcc hep transformation were generaUy in good agreement with the experimentally determined lines but the width of the two-phase field between each set of lines was too narrow. 

Since the thermal arrests were within 1.5°C on both the heating and cooling curves, as is the case for pure metals, the liquidus-solidus line and the solvus line for the bcc hep transformation were drawn as single lines. The transformation temperature of terbium was found to be raised linearly by the addition of holmium but at a greater slope than the melting temperature. Extrapolation of the transformation temperature curve to the solidus showed that the two curves intersect at 90 at% Ho. This confirms the absence of the bcc form at high temperatures in holmium. 

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